{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](https://github.com/callysto/callysto-sample-notebooks/blob/master/notebooks/images/Callysto_Notebook-Banner_Top_06.06.18.jpg?raw=true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions are arguably the most important topic in the secondary math curriculum\n",
    "### A function accepts one or more inputs and returns an output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25 1 9 49\n"
     ]
    }
   ],
   "source": [
    "# Here is a function that takes in one input x, and outputs its square, x^2.\n",
    "\n",
    "def f(x):\n",
    "    return x*x\n",
    "\n",
    "print(f(-5),f(-1),f(3),f(7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24 0 11 27\n"
     ]
    }
   ],
   "source": [
    "# Here is a function that takes in one input x, and outputs x^2-1 if x<0 and 4x-1 otherwise\n",
    "\n",
    "def g(x):\n",
    "    if x<0: return x*x-1\n",
    "    else: return 4*x-1\n",
    "\n",
    "print(g(-5),g(-1),g(3),g(7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "26 5 7 15\n"
     ]
    }
   ],
   "source": [
    "# Here is a function that takes in one input x, and outputs x^2+1 if x<-2, 5 if -2<x<2, and 2x+1 otherwise\n",
    "\n",
    "def h(x):\n",
    "    if x<-2: return x*x+1\n",
    "    elif -2<=x<2: return 5\n",
    "    else: return 2*x+1\n",
    "\n",
    "print(h(-5),h(-1),h(3),h(7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's plot these three functions f(x), g(x), h(x)\n",
    "\n",
    "### To do this, we import three Python libraries called \"numpy\", \"matplotlib\", and \"math\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe020458860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from numpy import *\n",
    "from matplotlib.pyplot import * \n",
    "from math import *\n",
    "\n",
    "x = linspace(-5,5, 100)\n",
    "y1 = vectorize(f)(x)\n",
    "y2 = vectorize(g)(x)\n",
    "y3 = vectorize(h)(x)\n",
    "\n",
    "plot(x, y1, 'red') \n",
    "plot(x, y2, 'blue')\n",
    "plot(x, y3, 'green') \n",
    "title(\"Comparing our three functions\")\n",
    "xlabel(\"x values\")\n",
    "ylabel(\"y values\");\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenge Activity: Make Your Own Shape!\n",
    "\n",
    "### Define two functions f(x) and g(x) so that the plots of f(x) and g(x) form the object of your choice.\n",
    "#### Feel free to use whatever functions you wish, including sin, cos, abs, exp, and log."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfedc1d518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x):\n",
    "    if x<0: return x*x\n",
    "    else: return 3*x\n",
    "\n",
    "def g(x):\n",
    "    if x<0: return -x*x+30\n",
    "    else: return -3*x+30\n",
    "    \n",
    "x = linspace(-5,5, 100)\n",
    "y1 = vectorize(f)(x)\n",
    "y2 = vectorize(g)(x)\n",
    "\n",
    "plot(x, y1, 'red') \n",
    "plot(x, y2, 'red')\n",
    "title(\"Our fish\")\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenge Activity: Turn the Sad Face into a Happy Face.\n",
    "\n",
    "### Play with this picture below to make the eyes, nose, and mouth look different.  Be creative!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfedbce550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f1(x): return sqrt(36-x*x)\n",
    "\n",
    "def f2(x): return -sqrt(36-x*x)\n",
    "\n",
    "def f3(x): \n",
    "    if -4<x<-2: return sqrt(1-(x+3)*(x+3))+3\n",
    "    elif -1<x<1: return sqrt(1-x*x)\n",
    "    elif 2<x<4: return sqrt(1-(x-3)*(x-3))+3\n",
    "    else: return\n",
    "\n",
    "def f4(x): \n",
    "    if -4<x<-2: return -sqrt(1-(x+3)*(x+3))+3\n",
    "    elif -1<x<1: return -sqrt(1-x*x)\n",
    "    elif 2<x<4: return -sqrt(1-(x-3)*(x-3))+3\n",
    "    else: return\n",
    "\n",
    "def f5(x): \n",
    "    if -3<x<3: return -(x*x)/6-3\n",
    "    else: return\n",
    "    \n",
    "x = linspace(-6,6, 10000)\n",
    "y1 = vectorize(f1)(x)\n",
    "y2 = vectorize(f2)(x)\n",
    "y3 = vectorize(f3)(x)\n",
    "y4 = vectorize(f4)(x)\n",
    "y5 = vectorize(f5)(x)\n",
    "\n",
    "plot(x, y1, 'red') \n",
    "plot(x, y2, 'red')\n",
    "plot(x, y3, 'red')\n",
    "plot(x, y4, 'red')\n",
    "plot(x, y5, 'red')\n",
    "\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions are used to solve hard problems, taking in inputs to return an output.\n",
    "### This is one of the BIG ideas of computational thinking!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Go Oilers\n",
      "Go Eskimos\n",
      "Toronto Sucks\n"
     ]
    }
   ],
   "source": [
    "# Here is a function that takes in two inputs (city and sport) and outputs the name of that city's sport team\n",
    "\n",
    "def teamname(city, sport):\n",
    "    if city==\"Edmonton\" and sport==\"Football\": return \"Go Eskimos\"\n",
    "    elif city==\"Edmonton\" and sport==\"Hockey\": return \"Go Oilers\"\n",
    "    elif city==\"Calgary\" and sport==\"Football\": return \"Go Stamps\"\n",
    "    elif city==\"Calgary\" and sport==\"Hockey\": return \"Go Flames\"\n",
    "    elif city==\"Vancouver\" and sport==\"Football\": return \"Go Lions\"\n",
    "    elif city==\"Vancouver\" and sport==\"Hockey\": return \"Go Canucks\"\n",
    "    else: return \"Toronto Sucks\"\n",
    "\n",
    "print(teamname(\"Edmonton\", \"Hockey\"))\n",
    "print(teamname(\"Edmonton\", \"Football\"))\n",
    "print(teamname(\"Edmonton\", \"Soccer\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Can you spot the different FUNCTIONS that appear in the breakthrough technology shown below?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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0/JX5H+juWjlGkC9xdWqOxfKR9nZQNyO0Ddeanoi0ukyi3dXDaPMWywqtf7EeatKtX+xHmsVsb0ZyEIWhkCEIQB1HYI2xWU9GH5FYLTfMepK2+xLstdUO6QuP4FYUY7gPxQBewzWs8mlaSzsJ/wAW49GFaSuGyxEJULUBElkqLKWhjUJ1kimhiIslQkAiAlQigEQiyWyloYiRKhTQCISoTSAEJUiYCJzd0iAlGVMCU7JqTMUi2nlT0JKgKsGN0VJDLc2fv4Ks71StxsLZ6RsL9AWi3gVkly2KUuJlB7gbh7vipWtlmtckjxUMsbqeV0UnrN59VZp6izQwkW5LDJGtG0JWaFNEGMGis2UEDtQtOGGwDnjXkFhixOch5MigiCeI+hOiHrOIf8Nlz2a3eHPVdVa8zb9VyTj69tsx+a9dVBUcEXzY8zGyiL7ph3SXRzNVGiQOUjZCq4KeDoujHK0TJErjcKEpcyDqoewSoba6aWp4ClZHmCSjYOVFWyCFeZRvk9UaJxw96bxC+VGdZLlVx1I9m7U30dx5JfCw+VFQhNIV8UbjyUzKJo9ZUvHb2S88UZYjceS0MPicwkkK2yFjdgpAAF04sUYdlYc7lOiOVheNEyOmJLvdPyVhPh9Y+6fkqnCL7Z619Hn2xKtUGj5APsqqdz5q1h/tX+6vFl02ectlpVq/2I81aVXEPYjzWS2U9GchCFoZAhCEAdB2TdklrXdKd/8A4lUZnMkpaZzI2Mc1uV2X63iVZ7OuysxA/wDt3fIrMZ6gQNM0MJH08h/oWks7B/aTe6Foq4bGCEIWwxEJUJ0AlkJbIshxCxtkJ1kWUcR2NshOsksnxCxEJUKXEBqE6yLKeIxEWSoCGqALJLJyRZNjEskTkKQGpUWSoGNcO6V0EQ7jCNe6Fj0cBqK6ngG8jrLpIqZ1PII5QL5QQt8SOfNIY7CoK0sklu57dgNj5qvilBSl7aeN8cNV62UbAeKvVdUMPoppwbPIyxjxKwPSeO9pkhiDgwNJA1d4nxVzrRGPk+7OgoKIRxRuLxKSNHAaFXnN0WN2drnMeaOZpFPIbwPI0a7mFuka2tqFUEloyyN32VXkRtkkOzGl34Li2+zB5nVdpiBEeHVjzsIXLjQLNAPRTlZrgQ0hIWpx0SLGzpG2TuSELbHl4ktDb6pQUhCFXK2Kh6ngIB1VcKeJhcbBbwMp6O4wWjjZQRSOYC94zXKvS0sMos+Np+5RYS4PwyntyYAra45SfJiUVRz+I4e2J1wO6dlkvjDTsuoxawpgT1XKVVQGOK78GRuNs5JxalSAhRvlYzcqlNWON7KpJK5x1KqedLRpDx29l+Wta31UUdQZXuuVlE3To5XRG7TZZR8lp9nbixxg7N+9lLTgveQ0EnKfkufNbKeau4djT6OXM6MPFjz8FpLyotUjrll66OPOrj5q1Qe3fz7iqnVzj1Ks4fpM/wBxeZLts5UXVUxD2I95WlVr/YDzWS2W9GchCFoYghCEAa+Buy0+In/25VJl8g05Kxhhy0WIH/kgfioATlHkgDQwke3POwV8KjhAuJz5K/ZaYygQhC1GCEqFaECEqUBaqIhtkWT7Isq+MVjLIsnWRZL4wsZZFk+yLIeIdjLITrJCFEo0OxqROSLkmWgQlKRYjBCVCQCAJbICEAXcE/jtB/1D/wCJXWVsZLGytFzHcEdQuUwMf7+oPfd/4ldo42eB1JXRjOTO+zInpG12Hyuc3M24LFz8jInYiWQXbHe1+hXR4/Xigo20kAAnmFrD6jeq5ymZkmaOitfZhC0rOiweKOowaOkmF2sJaSN2uvoQr0LnEPjlN5YdHH7Q5FZODSugxSSI6xVDfg4LZdE59Ux7CAQMrr8wqfTMZGf2gfw8An6yvbGPiuZhjMkos27QdVudqZB6PRU4+tI6T7hoFm4W0OL817E8ly5pUdmCPRWqqd0bi4NOX5KvZbc0LS0sJdYrHlZwpHMPJYwnZs0RoQhakiosgJRqVrElihlzotGljDQDzVWIW3VqKQNC649HLkbOiwWsbDeGR1mE3aTyK3M7bXuLLgJanLsUrcUqGty57jxUzxKbtExckjpcXq2vbkadG/NcnV3c8lTGtdL6xUclnBWqjGkJXdsz3hREKzI3VQOCymjqiyMpqcUi52ajUo3+5IlG6QGKbXOnNWcP9u/3D81XN7nzVjD/APEOv9gqSVsuKriHsB7ytKriHsB5rNbKejNQhC0MgQhCAL1E7LQV3ixo/wC5RtBI0BRTm1DVeOT5oBIHMIGamDi0U+nMK8qWD/4aY/1j5K8rgUIhCFshAlCRKFpEGOSgJAngLrxxshgGp2ROATrWt1Oi7FFJGLkR5EZFtQYHVktL4hZw67eabU4LVMqXRxRZgGg3vosvlxXVhbqzGLU0hWHNyucxwIc02IPJRuC1pNCUiEhNT3BNsuHJE3Q1InFNXnZNmqAoRyQsCgQlQgBAlQlCAL2Aj/8AoKH3nf8AiV2eXPMwHkSVx3Z8X7QUngHn/tK6XFZ/Q6KeoB73DLW+ZW0NHJlVyRzVXUem4lUVJNwXlrPIJtPcSEqCnIZGGqxEbLbGVLovwG9ZG8ANvINBsNV0h7spt4rmYnhskdrOeXDK29rrYgxGLjhkzmM1tq6xSm0n2ZOPIwe0kmbF8l9IIWs+/cpcKGSlaXtIEly0kWB8lWqoH1uNywzgs48uc+LPBdLV1D5aV0cNOGNByR522IH5Lhy9o7Mb40Uw07cllYpCdJNNDY2WtE6/dfa40UM8LZLtLCQei5ISpnRJWjnEiklZw5Xxn6psmLuXZiwCkjHNRhSNNgrTohkgNio3Sm+iQuUROuq6VkJ4j8xcVYawZdVCwtCfJKMtgVtFpIzknoa4hp0T2S6aqsXIDlm5j4E79VA8Jwcg6obTGlRAQmlTOamOasnEtMiStHeS2StHeU8SrMFx7x81Yw+/pB90qu4d53mrGHf4n/SVlJErZeVXEPYDzVtVMQ9iPNZLZb0ZqEIWpkCEIQBYhP8Assw6ub+afZQxeycOrm/mp0AauEaUcnjJ+SuKphelEfGQq0qiWgQlQtUAJQEWKULaKYmKFI0JgUrQvQwoxkyxSRh8tnbLZwrCo6moMrnENjOgHVY1LDJUztiiDt7uI5BdzTwwwxsEQAAFrjc+ax8vK4dJ9scJx41RIGvyi5BI8N04tvyUfFYJOHfvWvZS30vdeUyU0zjcdoJaSsdM9wc2Z19BayynBdN2sZ9BDKXm4flDeq50t0Xt+NNyxpszlSfRWcExTPaoyEssTaLIykSlIvJybN0CRKkWDKBKhCQAE4JEqANLs2L9oIPBj/ktPtRJfCIRzdPlWZ2bNu0MHuP+SudqXkuoqdo0AdKfktY6Oef+zDburcQ0VdjHZtlZaCBdbYk0PI7FkzC0rCM8Nn6jQea2Gxw8UMdWUxD+84nl9yxBWPhc+zGPY9hY9jxoQVeooKCqpqh74DFUUzbjiSFxk03sVnm7FFdGqXwwxCemIqHscWQZxYNIbd2XqpzWymCKdsoljlAIc1oC5apllpo8OLJDnZGZHC+gc4n8ldoJS6iIc90UMVha+mvRcWTXRtGJdqWHiCVhLidwRayWK7xroVWlmEEwj4he06gu6K4xw4eYbLkdpnUtHP4o21WXA3uqa0sTZmjMlhod1mld2J2jCaBIXJLpq0IoUlI7ZCkhEZlAl9SyaZVEN0XT5AwPOQ3CCGZL31WiFQy6LpqLpWKh19U9puownA2WkeyWiSyc2LOow5TwO7wXVBJmUrRG+nLUR073OFmldDhOHtrZrO9VupXQtwejbrkNxzupnLHB0zOM5S0eLvHecPEqfDtKr/SUyqbw6yoYNmyOH4p+H/4seRXDLZ0xL6qYj7Ae8raqYj7AeayWy3ozUIQtDIEIQgCSP1f9Q/NT/eoI+XmpzdAG1hTf93tvzeVcDQquG6YdF5kqyu3x3FLtA7HhgS5AmApcy7ozh+ENMeGhOyhR3SgrVTi/RLTH2CcAmgp4K1M3ZpYJWxUMkvFuA+1nAXWoMeg4D3ah4Jsy265q6W658njwnLkzJpnRS4vSOdA8kuN7mw1YnDH4DO8FruGBp/V+i5tF1H8mMcVx0Wq+tfXTZ3k5R6rSb2VVF0hK6YxUVSKdsQ2UMtlKVC8aqcrqBpj2QlIpCE0tXiZF2daGlASlCwZQiVFk6ON8pIiY55G+UXspbAalCQixsQQehFkoSsC/2fNu0NH/AFZx/wBpU+LVMdZiUj4nZmRtEQPluqNFUeh1jKkNu5gcG/eLJtOMkXUk3JXThfZlOPdkthdShoskp2GadsTRdzjZSSNMT3NPI2XWYPdFWpY0ssPWJAHxT8YfxMTdY+yY1gPkETOb3T/UD+KqTPMkr3ndziVy5mb40NMhLrvAk0sA7ZXpak1tc58cbYWS6ZL2bcBZ97OBG4NwpnVDnQuBZGHukLy8Dva8vJcrVmy6LrJOJSucHXdG8XzHUjwV2KoPCtosJjrC1lagmA0WGSHRtFmhNGJYiDzWG4ZXObzabLo6UiQBYeItLcRqAeoRhl6JmishCF0GQiRyVIUwGoRcApCgAQhCpAATk0Jy3i1RDAKaI2IKiCs08Re5b42Zz6Ov7KWdTzv55gPwW/yXN9npRTzGLZsg/ELpFz501NkY2mujxCsgkfiNWWt04z9fvTqOF8VQ1zrWsV1ruyLxNNLU18MLXyufYDa56myrV2G4NSUc3BxT0isDfo2Bw1PkFyPNHlSOlR6MdU8R9gPeVsXtrvzVTEfYDzTWwlozUIQtDIEIQgCSHVw81YLfEKvDupzsgaN6hGWgg8lOoqQWoaf3FItccqKFQkJyi5VufDaympfSJockel7uFxfa4W3MllZOCaDfmnta5xIa0uIaXEAX0HNdEJexMcE66SRj4mQOeLNnZnjN9wmZvFdcc0aM3ElQmG7XljgQ4bgjUIurWSLJ4D7pbpgKW6tNMXEW6EsbXSytjjaXPebNaNymZgb+BsUWtC4ilRvTyUx2qyyyXGjSKIyExSWsmlePlR0IanRRySuyxMLz4JRFJJLFE1pDptW3G46rZDYqaMMgHdI1d1XHOXFFrsqQ4S9xZxn2Lj6jNT8Vv09KMOpnmFmVu7g3UrNp2Vc7y+nsQzc3VyDFXRuyTi52N1xzlJmyX4Plio8TjaKhgdza5ujgsbFMEmoIjPC4z043Nu8zzWjJQGSXi4dUtYXaiF+1/Aq7Q1xAdBUx8OZgs9jjv5Jwm4ilG9HIXL2A7jlYK3DTPfTNlbYt5+Cs4thQpKyGaAn0Kd/faP8AL6jyVqpqIjhMgpGtjjD+Gxtt3Fd2KdvozkurIcMa2KI1Tz6xs1R1tuK4g6HUJ9c5sRZSR+rC0NJ8VXlcDGCvRvo8+m5WVJiq5Ush1UJ1XDlds7I6ERzSoWRY6MZn/cSla6xRCbSebSErW5udk6tCumaWH1NnBpcqmJuD6t5GxN/NRRv4ZUcrs7ySpUFEblYxISlSKhDblKClsEaBADSOiMpU9OGukynYqz6PpcLrx4OcbCzOylIrMrHA2soCConicQGoCVDQpiJj2C5WnRgCyoMFlZjly7LsiujmyJvRqifhWcNwtSj7QhxDJAL7XXNxh9U/LqAnijMUre/daPHyXZCwyguRx+ISumr6lxc4gyuIBN+aShNqyPzTZ22qJRm+ufmpYYhHVwWka7MA7RebLp0dMbLztyqmI+wHvK27cqpiPsB7yyWy3ozEIQtDIEIQgCWDmpXbFRwc1I71SgZ0UAtSwD/lhPukaLRRjowIVRZQoBc9gZ65eMvnfRdFJQsxCeOqxGB9HO2ZkcoLu5UDlZc7ZSSSSSholke8N9XM4m3krpsTRr1dNPVUE7ZMPjp6ptVkpWxtDS9g389L6qDs9I5tVXBkTZH+ius0tuSRyVSKtqIZxMJXOkDCwF5zWB6KGF74HB0L3MeNnNNiqppUKjeaIphQ0M1LEQcNdIX5bOYdNB03SyUMEGGtEkEXHpnQnMIiASSPrH1t1hcebPn4r82XJfNrl6eSV9XUPhEMlRK6KwGQu0UU/wBFRexVoqe1XAlYIGPkawuaLZx1/JW200NXLMyTDxSCmrGRRu1HGbexv101WJNPJUPD55HSPaLBzjqFK+uqpXROkqZXmI3YS71StO2lTHRrQUlHiMzfoBTMhrZISGE/SNa0nX71Qxr0dvoslGWMdJcSBocGDWwIzBVm1EzbBsr22k4osfr/AGvNLU1M1Y8PqpXSuAsC7kFcOSd2KjYiZT03aOmoY6NwMLg70kuN39wk+H/4oYKelrPRayKmEUOafjMdKctmm2YnffkqYxOtDImekvLYjdgNtNLKOCsqKYRiGUsEZcWiw+tupanuwo0q2moKIVtW6F00McMEjI2vIF3uI33tskqqKjoHySyxTTsmqWQRxteRw8zQSb/es6pramqZKyeXOJQ0PuBqGm4/FX8OxRrHyy1lXOyVzwS1jAWvAGnkfFQ3L2wotDB6GKaYzvHDfOYmB02XhgDl1N1l4GIW1+IMqGcdkdPLlIO7Rv8AeQlbjFWypqpYnBrZ5DJkc0OynbTxVWkqJKKp48BGexBzC4IO4Knv2VTNdgpnxUAjbK2rZhrpInk3a1oGxHMqR9JHHRU0s3EbIySITRF7STmIFrDbUrKZXTuqo3ktDhEYBZtrMKdU4rVzwGCQx2zNcXNZZxLSCCT9wWbS9hTNOJsrcak9CL4qV1Twni40dzsOidM6LEgeE2STJU+jvOQB2gvmb8Oao0eLSOxWOaocyOJzw6XK2w05+atCtdNkkikiieyRzwwRgMeTcd4c9Flxjtl3L0T8EUM7pDO/0ZtM6a1mvcCDYjTQpsxgnfBJC57pZaN8ueVoJy2NvLf8AqsWJyNqmMqI4YWsbwwxjLNy5gbD4LSfB6SwOojCHtjexokbrld9UEFK8aBqe2RMaRBDhVRI6V89myO4V2NOXNYO6qthdpKSCRwZltUNy2+zpdNjxF8UrYsRaIKinAcH27zyBYX5G6rjF3lrAylgha1sgDGXt39ytYJehS5EwwuU4bTVPFe6SR0Yk4kZb6xtpz0uq8kccGO0lLFLx2ioa2QltrHNqPFTy4u/htzUsYkeY3OkDjd+Qi3lss41B/eTazLqJ+Pkvzvey2uS2ZpF2XCI6quk9DrGSNNW6KYcMjhE3IA6pKfAhUl7oq0PizmKN4hcczxvfoL6XSjGmRzskp6JkLTMZ5gHXMjrW+7dQ4fijaSlfTzRSSM4rpYyyUsILjcg23Cx6K+xGcHlOEyVnGbnhu6SMMNrNNiM211N2iw/0OpqKoGONkkjWwQN3cMoufDVOOMMdhZppIJDK6AwFwk7tutuvio8YxOLFY3cSAtlY8GCQWu1ttWnrzR0H2LGGYbTOOETGZkrqkSZ4zex0Py2UEWEScaKJlRDI2RskgmDu7Zps4Hyukw7Eaelp6Js0MjpaRz8rmkWLXXv+SbR4hDT0EVO9jyWRzsJG30hBHyR0HY5uDVErMzJacufmMDOJrM0c2qr6BMZWx3bmdSel6n6vTzVqir6OKGglqYZnVuHxGOEsIyOFrC6c3FKL0Xj1LZhWiiNKcoGS3VHTC5FafB6yKhfUOMTeHGJZI8/fa3xCmxzCZaKeqqYms9DYWWa193MBA1I6XWlWwtbSYpiM0E8NRUUYY7OWmMmwsG23usyqroJ5cae0utWxxCK45tABuikFtkNNQSVmH0r6aNzp5p3suXANIaLofhNc2sipeBmklaXNLXAtsN9dlawavp6Oio4pnODoppHus29g5pA+aMOxCmhwqlop3vbeKWKV7RrHmNwUUh2yu3Cq+LiyOp7sgNnkPaeQOmuuhVySkqYDC2WB7TM7Kwaam17eB81V4tNQYXFS0s7qng17Z9W5c7QBf8AFbE9bSS1EbuJFJTy1HFe1sBa5vdIBcb662XThyzgqiHJlF1FUGrFKYH8Ytz5bcut9lB6BJKyZ7IHkQkteQ3Yjda7qqJ1RTNFVT5GwvjmHBcI3guGgG40vZFNV00cLY6aSKMU8khb6Q1xLg7UEWOvTVavyMj3EOT/AAxqDCX1kjXlsgpnMe4ShulwNFRghe+JryLXF10dJPG6WnqnVjYWMpOA6l1Hft02ss2nbkgY1w1DdU8cPkk7Q4xciiWFvJRh5a5abo2u5KI07L6jRb/C1obg49klPUMZHcjVN9IvIHE+Su0eF01QLGQtPgVPP2YcLGCpJ8HInPj9TDJn5dM84qNaiU/1n5qw1uSopTlIBANzzUNWwx1k8bt2yOB+Kcwkz09+VgvLns0iaTvWKp4j7Ae8rj/XKp4j7Ae8sVst6MxCELUyBCEIAmgNrqQuO3VRQ81K0XkYP6ggaOldpYdAEJ0ntCmoiWSU0YnrqWA3yyytabdCVtMw3Dny1UlpGw083AyvmDczuZufksSGR0FRHOy2eJ2ZtxzVmnxKpp5J3t4bxUPzyMkZmaXdbK2yWmWKukw/C4hLUSTVTKiVzIOE4WA8TzT3YZSiabDWSTGvjp+NxTbhk9LKrHitSyGSJwikZI4us+MHKTvbokmxWrlozTlzLuYI3Shn0hb0ulYqZblw+ib6fSsfUGrooQ97zbI5x6J0+G0jaiaKllnE9HNDnc+xacxG3xU1bicLaCoaypiqZp2tY0thyO05vPNZgxKfj1MxbHnqHse/Tmy1rfBKw7NaeGnzxE8T0l+J5BNlbckdfCyqOoab01kdbUTCpxCaTg8NoytAJsXf/CrsxadpcTFE8mfjtzD1XeCWLF54mWMUMkjXOdFI9t3RZt7JhTLMWDwf7PTy1EorJ4nvAa0ZAWlZ2ExwVdPV1NXK+GGmjD3FguSpYsTmjnpZi1rn08LoWk/WB3J8VVgfwKGqpGtBZUtDXE7iyfJjpmocGZ+7mVZlqGgFj3B0YF2k6gC972Uz8HhqsUrTA6ZtPC5sZYyO5zkcvC1iqk2MSTUr4jTxNkkY1j5he5y7aJTjGaaZ0lFE6ObKZI85F3j61/8A7si2FMdLg4pqOpmqKhxdE9zG8OPMBbbN0uocPbTSdnq59ZNwIxUMHEDcxGg0CWPFOFT1DI6SNks+YOkDjsTe1udtrqGgqoKWhko56NtVDJIJCHPLdRa3ySsO6LUmCysngibKJC+p4MhA0Y3LmDvgqtDStrsRnpmSkRxXs9rC4usbbBXo8Qmjw/Eq+WWPi1pDYYWm5YQMt7ctFQwqqbh4nY6IyxzsDXBryw6eISsOy4cHFO6d1XWxwMinbEHFhOa4BHzQ7ByMzqusipzxzA24JzHS1vO6nlxGlqMOkqauj4gfVtcIRLYtytAB8Rog18U2ExVldS+kPNa6UMY+3DI0bfw2QHZUGCT8FofNC2pkldFHCb94tOuvkLpzMMcJYzTV9PLG95hL237sgFw377Jj8XkdLRVGS81NNJK7XR2a+n4p8dfh1PkipqKRkAlNQWufcmW3d+4KaQ7kSvpZjSPiqWxOnHBBbmN4i91rFOjwqrgmBirqTKJOHrIdH8m7bqI4rA975nQvbPO+F82W1i5jrkjzAUPp8V75H/xH0v8A03280uMR8pFvEfTMZw5jwKds1GZM8Zk75LdDpbQaKCpwl7amFlPPA9jqcTSvfJYM8Tp6p5K3HjtMIpWlk7C7ijI0DK7MSQ4876qGkxOniMTzx45H0jaaZzADky7ObffcqlS0S7GR4PUPoqmFzWCrbUNETs/dcwtvp56rLljkZRU9SQGtqJDGwONjcGxJ6BbD8Rkqn8CkdUT1LqqKSIvaAcrRre23P4ql2lkbV4pJBDYQUzeGwDbMdXfinYKy87ACySthD2SPbTMfCc4GV3O/gqIwudsFVFJE/wBLZJGxhDhkOZWa2spJ6atfHJIJ6ujbAWFujXN8fvVluKUYDPpHaej37p+p6ymkFsqDs9X+iSyOY0TNeGtjzt1HPW+izHwyx0888kZbHBLwXk8ndFdFRE+kxeEzuZLNVekUzg0uLiNQPwU3ayoD+BStj4Zc30mdvR5FrJUhpsp/uytNJ6UKZ5hycTMLer1sozRVYo46o00nBkIDXW3voFuGWnpYsMrJqstkhoCG0wB+kJCdNilPJRxyxzU7C9sTHxFh4gsRfnaw1RxQcmYhwvEBOIPQ5uIW5gMvJQmlqfR5pjTS8KElr3ZdGkbrXmqWVsmM0jcQ9FdPO18NQXHKWi3dvyVmKvgbhTQ2opnyU8T4n8V7gXnqG7Oujig5MwZ4K5lOwywVJizNDA4EtudrIr6SbDqw09Q2xsCHcnaclr11cHy4ixlUHRfuxvCaH6cQdP6lXx6F1SZ8VFZHNTBsTY2B2YgkWI8DzRQKRUpcPnnZSTZS2nqZ+CH2Nx4+SrTRSQ1DoXxvB4jmMu0jiWNrjqtnB5XyYTRR+ktb6NXB0rHvt3CdNOYvZWKOpNbJesqu/FicnCdcAhuV1gPA7IoOTMCOmnkNQ1kTs1PHxXtIsQP1U0zZaSaKIkPMkLZhkubArppppjiDGRSNiqZqF7bcUO74Ol3cyLlZfZN1S70yNxcH52sdMHNzxkeB0LVpBuGg5MzmVYNgeanjmZI9jGuGZ7wwa8ybI7OseMari15c+Jj8nDDbynN9W+gS4+0R9raUtbkD+C94/qza7Lqj5Mlsv5GS2/2l1PccRspiOvO9kju69zToWkg6rWqWTurKo18ETIW1kPobg0Auu4ZvPS6Snie2rpY6Skjmp5KqYVTiwHIQTYeHJUvLftAsplJCq7ahjZp4724cr2/AqXiNdsV2Qypm9poS5abtJB8FagxCqa9reKSLqm5LAfpmea2lTXaORwTZyWIXOIVJO5lcfxTGAiWC45j5p+I6YjU/9R3zV2joH1bBOx+eGliD5D9k39XzXgZXUmNIlf65VLEfYD3lbJzd7qqmI+wHvLJbKlozEIQtDIEIQgCWHmp4BmqYR1ePmoIdirVEL18A/rCHoEdFJ7R3mmpzz33eaakn0aElPDJVVMdPC3NI86DkPErTkwkjCoWU7oaipmqsokjdoAL3BPhYqjhtX6BiMdSW52gFrmjexWhT4rR0ApoqGCbhRyve/ORc5gb2+KZLsrPwmZlREzjU5ilaS2bP3dNx5pZ8PdRYViRqGtM8UkYjeDplNtlcbjNOJnAvrHsMeVsrsudhv9UbBNq8VoqzixzRzmGWRhdtctaP1QHZioQbZ35b5cxyg7gckJWWCEIVWgBCEIsAQhCVgCRKhJjGpUWQpAEud2TJfu72SFIk2MEISpAIlQhAAxpfI1jRdzjYBO2+5OpZBDWwSucWtY8EuHJaWOUYAdiFPkMZP0zWbDo8eBVJdEN06Mtr3xuD2Ocx3JzTYpnNK55cGguJDR3fBNClsuhyRCEgBrnRyNew5XsN2uHIpJXumkfJK4vkf6zjuUFNTsB8sskwjEji7htyMvyHRRpUiQAiyEBNAIjM4MLA4hhOYtvoT1QUiYhLAnZKQLbJEJAKAE4eGiaE5aRExRoQRoRsRokJJsSSSNiSkukWjkIc6SR2XNI92U3F3E2PULRw3Fo6GJpdSGWoa4uEvFIDiebhzWYkUhVhclz3uN3PcXOPUlAe4bFIgp20WSCoeOangqrSNzdVSSt9YLWPkTXsVGPiJzYhUEc5Db4r0XAMJZR4W6lkYCXsMk46uI0H3Lluz2GNrcanqpm3p6dxOuzncgurqsVGG4XLNJGcwFtT6zivO8mblJRRUI9NnC05vCL8ifmoMR9gPeVmNmRljvuq2Jewb7y1WyJaMxCELUyBCEIAlh2Ku4YL4nTjxv8AgqUOzlfwgXxOLwDj+CHoaNx3rFIhCzRoTUUEdRUiKWobAHWDCWl2Zx2GiuvwhjX1kcdWJpaRmZ7GRm9+QVGjAOJUdyABOwknkLrSFS6GXtLUwShsry1sLgdTy0VEttGUyOV8hiEUhlaLuZlNx5hWKahnqYYpmMtHJPwcxB0PXyXSxOjNX6Q2oa6bhwtkbxcgI3Liee+yzsVlklwmuFNUANjrXOc0Ptdlth96KFyMaWB8c1Q0Bz2QPLHSBpy/FLFTSzUr6mNl4mSNjJ8SVsd7/wBJBr5RAGxdzhyA8W/1XN6qDCHTvwGWCKUMLaqNzml1rR3Gb80UPl0Z9fAaKsmgcSWxkASWsDoojdtswIzai4tddHJVNqZ8RbXSNfSxVkAjabWAuL2+9Qdqnvdh/Ccw5zOXROMgcQPADYIoFIyaCmdXVsdMx2XPfvkaCwun01EZ3A+kQtiFPx5JAbiMXtY+K38PNQw0TqWSNuGNozxG3FzL487qq6ompMNnNPJkdHhTC21vXuVQuTMerpjSRUxkljMs4zcJt7tbyKr529QutE75a6ZueSSojpYjEIy0OF/WLc2l9lWrqrgU8jmMEDZ65kc17E5SAHeGqVDUjm8zdO8NUmZv2guxmDfT6WKSmk4ban6B7smRrQw+rbW1uqpUbxiDKWpq2RuqGTzspwWgA29UIoOZzeZv2gpqOB1ZVspoiM7wSCTpougwv0x0c0+IUzv3kHNaWxRsLuF5E2te+qoYYxn/AK1l4MZYwZ8sZ5G2o+KKHyMdjg8XB52T2MdI2VzAXNibmeR9ULpaSDjvpJcUpmRYg1sxjiawXLQRbu8/BEkrmfvEUlKfSTRskdG+ENMjrkXy+XJLiLmcwCCLgpV1DKChqtAGA12SrbpoGNy3HzTA2gmwv0gU94quOSVxZAXEHl3h6tkcQ5nNpF0tTQ0EcEVNwbtaYSx7YXakuGpfsQbrPxkQPw+ulipYoH0dYImGMWzA2vf4pcR8jLA1W3gklQcOqqeKLjsc1wLMwBB5WulwqmhbFhUZoGVIrQ580zgSY7C9h0VilwulNHFCImOZNd7pMxztJvq3oG2VKNEydnMmKSBkbJWOY5zA5ocNx1QFuStpqehkrKin9JMFFC5rXuO5vdFVRUVA+ed1I6pbLURQshzECIOa0k6eZUuJXMw0itYpEynxqsghGWKNzcrelwq1lD6LTsRIlQkA1CckKBjEqEJoQJCE5IrAbZCdZCKAaAlRdCYhEISIAVIhBQAiRCE7ARNcbNJHIJybJ6jvJFjOuwKlZHg9MI2m0o4jzzc4rmu2mIRyVseH0/s6c3kPV63JcTbhfZSjmb7XghsY/qXnznue8veSXONyTzWGPH93JjnLpJG3J66o4j7Ae8r0nrfcqOI+wHvK1siWjMQhC1MgQhCAJYdnLSwQXxAnpGVXwqi9Ne9vEyBoBvlutqDD4qA8Rj3ve7um9gs5ZIp8fZcYt9kyEISLBCEIsYWHRCEIsKFS2TU7cIsKEQAhCLCgSpEqLCgvre5v1RytySJUWFC3OhzO7u2uybc6C50NxrsUpSI5BSHCR4fnEjw8i2bMb2801pLXZmuId1B1QhFhQ50khkbIZHmRuzi43H3pRPNxTLxpOIRYvzm5HS6jQlbCkSNmlYWlsjwWNyNs46N6DwSxzzRQOgjleyF27A4gH7lGhPkxUiYVVQIWQieThRkFrc2gI2THzyvjlY6RxbK/O8H6zuqYhPkFI2MIxGGipGNAqBI2+mf6NxOxIUTsRqBRtjjkcyQvvIGC0bh0y/NVKMBz8rnBrep2Su7zjcABa+jJ7HVNdJU0roXj1wGv6OaNgrOG4oIpJZauqqmSuc03ia0h7QLAEEaeYTYxBwg/KDbe6zXm73EDcqZWhxpj6uY1VfUVRGUzPvboNgokqFi2aoRCEFIYiRKkTARIlQhACEJCtBAkTZHFrCQLrbqez0zJXNgnZI1sTXXf3buJIt+CBNpGKhagwKqfnyPiIZJkJJI2Gp2R+46iN49IewNtJ6jrm7QSPjZHYuSMtItCDBquV0N8ga9jZHEHVrSbbdUPwp8DyKmQMaKhkN2jNcO2cjsOSM9Ir7cJne1xjcxzg+ZpBNhaM2Jv18FBJQ1UcZkkgc1gGa5I1Gmv4hA7RWQrlHhlTXUjqinDC1sgjsXWOttfxCK3C6qhgM04Zww/Jdrr6oDkikkOxSpHbG26Ch+KQ1FdQUVnMZTwsDGtJ1J5lZwwo31mH3BdHT1GAtwyCDEKyZs7Rd8bGnQ/BAxLsnCcwjqpiORv+qmc6dQQvr7MZxufLRU8S9gPeV2QATSFlxG5xcwHcNOwVLEvYD3kR2KWjMQhC1MQQhCANfs7W0lFVPkrWPfGR6rRutuqxqhxJjYaWmbSMidnLnkAv8FyUIJvZSZCspYouXJ7LUmlR0fGh/nR/wBwRxof50f9y5sxnokym2yvih8jpuLD/Oi/uCOLD/Oi/uC5myMqOKDkdNxYv50X94RxIv50X94XNcN1ibbI4buiOKHyZ0ueP+dH/eE5skf82P8AvC5jhu6I4buiOMQ5M6cvjv7WP+8IzM/mR/3hcxw3dEnDd0RxQcn+HUXb/MZ/eE4FpHrs/uC5bhu6I4buiOEQ5P8ADqLt+2z+4I0+03+4Ll+GeiBE4kADdHBByZ1Vu4HXGUmwNxukynkR8Qst0Ej+zcDLC4neWi+vIH5LKyO6IUUNyZ1OU+HxRkd0XK6jn+Kcxsjz3A93uglHCIuTOoyO+yUZHZc2U2va9tL9Fi0uF4hMM7I3Abd92Vb0VHJ/6Snw+QhtUagSs10tpzWbeNey6l+EeR32SjI77J+CzWYHiH1qhjPN5KnZglR9fECPdulzxf8AoOM/wtljvsn4JMruh+Cjbg+XevqT5Gyf6FFFvNUyHoZbX+Cn5cf6VwkPjkdESbaLQMDntjfl9o3MCNbhZtNS54yTxHPzHQOcQFdho6u1oqecjwBVR8iMeiZYW+yu93DLm37pUF1rtwfEH/8ACPHi4gKT9w1mXM8QxtGpLnbJSy8tIccaXsxEq134XDE28+J0TP8AUP1UbmYFGPpcbjd/023/AFR3+BS/TMSK+azsvFvU1c5/pZb8gonY72aj9TC6qbxeR+qai2S2ioUill7TYT/ldn4/9b7fJUZu0TXgiDB6KLx7xI/FVwYuSLCFk/vSqH1I/wC1H71qf5cX9qrh/wBDka6aVmfvecbwRfA/qj97y86eL8U+AckaSfxZLEcV9jv3isr97v5wR/EpRix3NMLe8UcWFo2I6ypjlbI2d5c1wfZziQT1ITZKuokldI6d+Zzi42PP/wCkrNfiQY1l4O84XIDtk396s507v7kUxfU1219Y31aqUd0N9bkNgmSVdRK5zpJnuLi1xJO5b6p+5ZgxWH+TJ8Qj96U/8uX8EUw+pptrqmN2Zkxvmc/UXF3et8U6oxCWdsbLNbHHAIA0ajL+qyv3lTfZl+AS/vGl/wCZ8EUw+po0lbPRxvZTuDA9wc7S+ykqcUqqqCaCYsMcrg5wDbajmFl+n0p+u8f6Vo0FBNiNMKimtkdJw25tLlJtrY0k2VUK1iuHzYOyJ9a+ICUkNyuvsqHpVP8Az2pIqzPxQWrneQVRWsSeySrLo3Bzco1CqrRaMXs3Dqxh/pCpYj7Ae8rrWuMERDSRkGwVPE2kQNuCO9zWS2W9GWhCFqZAhCEAPj5p6ZHzT0DC6LpzIpX+pG93utJU8eHVsjsraSa56sI+aTkltjSbKyRarOz2Iv3iaz3ngKxH2Yqt5J4WeVys3nxrbLWKb9GMx5bHI37QA/FMuV0kfZeMe0rHG/2GfqrEPZmhM0UZfM/M8N3ss/6sV0mX8GSjk7lF/Fd/X9n8Kp8TfHDRNytaNC5x1+KdHhcTRaGgYPKJKflRg6ocMDkrs8/aHO9UOPkFMyiq5PUppj/pK9DZh1TbuU5b9wCf+7Kn/MfGwf1PWf8AXJ/5iX8EVuRwLMFxF/8Awzm+8QFM3s9XH1nQs83rs5IaKH2+K0kZ6Zx+qrvrsBi9piof4Rtun8ueWoi4Yl7Odj7NPIvJVtHg1pKnZ2bgHr1Ep8gAtR3aDs7F6oqpj4Cygf2vwtnsMJe89ZH2T4+Q/dBeFeiNmEUbAATK8A3s6Tmp4sJogO5Qtd5guVY9t5NeBhlNH0uSVWl7b4u7SMwRD+mMH5prx8j/ANTG8sFpG7Fhrx7Kgy+UYCtswyuI0hyjxIC4uTtTjcvrYhKPdAHyCpS4pXz+1rah3nIU/wCRe5E/0fiPQn4ZKwXnngjHVz9lIcIDIjLJVNDAMxLW6W6rzB73Pvmc53mbr1jA521XZ/Dy7vZ6YRk+IFla8XGgWaTMV1b2ej1fijpPBjb/AJKu/H+zcXqxVs58rfmuKmjMFRLEd43lvwKYqWDGvRm8sv07N3a3CGexwd7j/wAx4/8AlQu7cObpT4VSx9LklckhaKEVpEucn7Okl7b4w+/CdBCOjIx+aqSdqsck3xGUeDQB8gsZCqkTZelxbEZ7iWtqHixuOIV6Xi4EHYuob0og34heUNuXgN3dp8V6n20cIeyVU0cxGwfEJgeVhxsEud3VNQi2A7O7qUOe6+6ah25QAuc9Uoe4c01CAHcR/VHFf9pMQkFk0krnBmuzbKMvd1SE3aEiAscSbXSslc08j4FN+qEiAskdM9xuTqk4rkxCKC2P4rkcQpiEUFsngm4by4sDtCPLRR8Q9AljtlkJB2tcclGlQ7ZZpIZa6ripYWgySuyheqYZRRUsMUEVhFA3KD8yuW7C4XlZLikrdTeKG/4n8lr9rsTGFYIYYjaoqgWNtuG8yuef2lxRrH6xs47tVi370xmRzNYIfo4h4DcrIzj7ITAhdCVKjG2Ozj7ISh7QRdgKYhFBZKZiPVLgOgKZLK57bOJPmUjt0x2yKBsahCEEghCEAbHZyCGepkE0QkAAIBF11cFGHewoGtHXhgLiMOrqige59M4NcRa5F1ZlxvEph36yUDo02XLlwynK0zfHkUV2jum0dVcZYgweLgFK+i0Bmnhjtzc9eburKp3rVMx85ConOc7VziT4m6x/ivcjX+l+j0d8mGQ+2xWnFuQN1Wkxns/FvWSSn+hhXn6FS8KHsh+RNncv7UYKwHhUlRNbroqzu28MbgabCI2kbF0mvyXJRXzaamx3TFtHxsa9EPLJ+zqp+3eIyOLo6emjJ55S4qlL2uxqX/iwz3GALCQtvjj+EcmX5saxOf2lfUHyeR8lUfPNJ7SWR/vOJUaFSSQrYIQhMQIQhAD4xcO8E07qSDZ45kC3xUbtHEeKCvQiEIQSC9K7CS8Xs3G0nWCdzfIHX815su4/ZxPeHEaY8iyQfiD8gmtji+zmO0cPo/aGujtb6Ukffqs1dH29h4faUvA0lia78vyXOJAwQhCBAhCEwLGHsz4hTstfNK0fivQv2gSFvZxzD9edo+AXCYCziY9Qs6zN+a7P9o77YTSM5unJ+AT9Fejz1CEJEgg7oQdykAIQhAAhIhADvqfemp7WkxPdyaR+aYgY7L9Hm8bJqfb6EHxKYgGCEIQIEIQgCaMD0aZ2cg6AN6paGklr62GkgF5JXZR4eKa3/DvPUgLrOwVEA6eveO8Bkiv+JUydKy1Hk6OnIZQxw0lN3YqdmptyG5XnOP4rJi+Jvnefo292MdGrsO2OKegYV6LEQJ6rQ23DOa89WeKPtmmWS/ygQhC2MASJUIADumu2T3aOTHbIAahCEhAhCEAT08YkZIeIxjmi4DjbMkzNQhAxMzeqMzeqEIAUFvVF2dUIQFj4jHm1dbQpl2dUIQOwuzqi7OqEICwuzqi7OqEIFYl29UXb1QhAWF29UXb1QhAWOa5oO9kPyB5710qEDvobdnVALL7oQmKx8hhuOGXWtrfqt/sPiFPQ40/0idkUMsLmlz3WAO41SoTCyx29qaKskopqWqhmc1pY8RvDrdL2XJ5m9UISBsMzeqLt6oQgAu3qi7eqEICzR7PVFPTY9ST1EgZFG+7nEbaFbXbrGKLE20DKOobKI85flB0vayEJ2O+jlLt+0i7eqEJCsLt6oLm9UIQFiXHVFx1QhABcdUXHVCEASQvYGTBzgLs087hR3HVCEgscZAWBvJMzDqlQgLEzBFwlQgBMw6ozBCEAWY+BJDBE6QMLpTncb90aartaHGcHonGKKrYIWANbodQOe3NCFLVlxm46OPxrE3YpiUtS42adGDo1UbhCFS6IbthcIzBCECC4StcMwvshCBiyOGd1jcXTCbhCEANQhCBH/9k=\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/Nu-nlQqFCKg?start=387\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fe024004eb8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('Nu-nlQqFCKg',start=387)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt text](https://github.com/callysto/callysto-sample-notebooks/blob/master/notebooks/images/Callysto_Notebook-Banners_Bottom_06.06.18.jpg?raw=true)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
